Skewness and kurtosis for portfolios?

I would very much like help on the following problem:

I have N financial assets with T return observations each.
I am to add these N assets into a portfolio, weighing each asset with a particular weight, with weights adding to 1. This is the easy part.

Calculating the mean and the variance is straightforward, but how on earth do I calculate portfolio skewness and kurtosis???

I would assume I have to deal with coskewness and cokurtosis, as with covariance for the portfolio variance case, but what about these two moments?

I don't know if there are formalae to calculate kurtosis and skewness from data, but one way that is often not very bad is to assume some distribution for your data (like using the skewed hyperbolic distribution). Kurtosis and skewness are defined for such general distributions.

Co- kurtosis and skewness I really know nothing about. Sorry.